1998/07/31 by Arturo Magidin
Mathematics · #math.GR #msc:08B25 #msc:20E10 #msc:20E22 #msc:20F18
published as Algebra Universalis 42 (2-3), 217-232 (2000) · Plain TeX, 22 pp. Typos corrected. Final version
arxiv created 1999/05/13 · arxiv updated 2009/11/30
Dominions, in the sense of Isbell, are investigated in the context of decomposable varieties of groups. An upper and lower bound for dominions in such a variety is given in terms of the two varietal factors, and the internal structure of the group being analyzed. Finally, the following result is established: If a variety \cal N has instances of nontrivial dominions, then for any proper subvariety \cal Q of \cal Group, \cal NQ also has instances of nontrivial dominions.